Motivation—Materials
that undergo phase transitions can dramatically change their properties
as a result of small external inputs. Understanding the dynamics
of phase transitions is an important step in the quest to understand complex
collective behavior. In many systems, phase transitions require the
transport of atoms from one phase to the other due to differences in atomic
density. In these cases, the kinetics of mass transport can be just
as important as the thermodynamic differences between the two phases in
defining the rate of the transformation. Although such diffusion
processes can be treated theoretically, they are difficult to address experimentally.
By studying phase transitions on a surface, we are able to quantify the
mass transport process and assess its importance in controlling the dynamics
of the transition.

Accomplishment—
We have used low-energy electron microscopy (LEEM) to show that adatom
diffusion controls the dynamics of the phase transition between the 7x7
and 1x1 surface structures on Si(111). The equilibrium structure of the
Si(111) surface at room temperature is a complicated reconstruction with
7x7 periodicity. At a temperature of 820 C this surface undergoes
a first-order phase transition to a structure that gives a 1x1 diffraction
pattern. This high-temperature 1x1 phase is a dense overlayer of
adatoms (6% more dense than 7x7) residing on the bulk-terminated structure.
To study the dynamics of the transition, we made real-time observations
of the time evolution of triangular 7x7 domains during growth of the 1x1
phase. Figure 1 shows a series of LEEM images taken as the surface
transforms from the 7x7 to 1x1 structure. The bright areas correspond
to the 7x7 domains. Figure 2 shows a plot of the area of several
domains as a function of time. We find that the domains decay approximately
linearly in time with a decay rate determined, not by the domain size,
but by the local arrangement of neighboring domains. This observation
is counter to the simplest picture of phase boundary motion, in which domain
walls move with a constant velocity (independent of environment) determined
by the free energy difference between the two phases. We have modeled the
effect of this mass transport requirement on the observed decay by solving
the two-dimensional diffusion equation for the experimentally observed
configuration of 7x7 domains. From this analysis, we find that the
decay is limited by the supply of additional material to the boundary.
Moreover, the analysis is consistent with a model in which sources of adatoms
are uniformly distributed on the surface. The model reproduces the simultaneous
decay of all islands in the field of view with only one adjustable parameter
(Fig. 2). The results lead us to conclude that random adatom-vacancy
generation provides the source of material required for the transition
to proceed.

Significance—This
work identifies an important aspect of phase transitions that is difficult
to address experimentally and therefore often overlooked. We were able
to quantify the role of mass transport in surface phase transitions by
observing the phase transformation as it occurs. In the process, we discovered
a novel precipitation mechanism involving the random creation of adatom
and vacancies at the surface and subsequent diffusion of the adatoms to
the domain boundaries.

Figure 1. Low
energy electron microscope images showing the decay of 7x7 domains during
the 7x7 to 1x1 phase transition on Si(111). The field of view is 2.5 microns
and the temperature is 830 C.

Figure 2. Decay rates
for selected 7x7 domains. The LEEM image has a field of view of 2.5
microns. Dots are measured rates from LEEM images. Blue lines
are fits from a diffusion equation model with one adjustable parameter.